Lesson plan Grade 11 Science
Calibrating a Nitrate Test at Marlow Water Lab: A Regression Lesson
A grade 11 lesson where students fit a line to a colorimetric nitrate calibration curve and use it to convert sample absorbances into concentrations at a fictional lab.
Objectives
- Students will fit a best-fit line to colorimetric calibration data and write its equation.
- Students will use the calibration line to convert measured absorbances into nitrate concentrations.
Vocabulary
Key words: calibration curve, absorbance, Beer's law, best-fit line, reagent blank, dilution
Teacher overview
A colorimetric nitrate test turns a water sample a shade of color, and a meter reads how much light the color absorbs, but that absorbance number means nothing until it is tied to known concentrations through a calibration curve. This lesson has students build that line from a set of standards at a fictional lab, then read unknown samples off it. A common misconception is that absorbance and concentration are the same thing, or that the line must pass through the origin; students should see that the small blank reading is exactly why it does not.
Procedure
Hook (5 min): Show two vials of water that look identical and ask how a lab could prove one has three times the nitrate of the other. Draw out that color intensity can be measured, and that measurement has to be calibrated against known amounts. Note that all values used today come from a fictional lab, not a real utility.
Direct instruction (15 min): Introduce Beer's law as the idea that, over a working range, absorbance rises in proportion to concentration, giving a straight line. Project the six calibration standards from the handout and model plotting them, drawing the best-fit line, and reading the slope as absorbance per mg/L. Show that the line's small nonzero intercept is the reagent blank, the color the chemicals add even at zero nitrate.
Guided practice (10 min): Work handout item 1 and item 2 together as a class, computing the slope from two points and writing the calibration equation A = 0.095c + 0.02. Have students predict the absorbance of a 6 mg/L standard from the equation and check it against the plotted point.
Independent practice (15 min): Students complete handout items 3 through 8, converting measured absorbances into concentrations, handling a dilution, and deciding what to do with an off-scale reading.
Closure and formative check (5 min): As an exit ticket, students answer one question on a card: a sample reads absorbance 0.305, so what is its nitrate concentration? Collect and confirm at least 80 percent of the class applies c = (0.305 - 0.02) / 0.095 correctly before moving on.
Student Handout
Suppose you work at the Marlow Regional Water Lab, a fictional lab. You ran six nitrate standards through the colorimeter and recorded the absorbance of each:
| Nitrate-N standard (mg/L) | Absorbance |
|---|---|
| 0 | 0.020 |
| 2 | 0.210 |
| 4 | 0.400 |
| 6 | 0.590 |
| 8 | 0.780 |
| 10 | 0.970 |
Using the two end points (0, 0.020) and (10, 0.970), compute the slope of the best-fit line in absorbance per mg/L.
Write the calibration equation in the form A = (slope) x c + intercept, using the blank reading 0.020 as the intercept.
A river sample reads an absorbance of 0.495. Use your equation to find its nitrate concentration in mg/L, reported to a sensible precision.
A well sample reads an absorbance of 0.685. Find its nitrate concentration in mg/L.
Suppose Marlow's internal alert level is 8.0 mg/L. Does the well sample from item 4 exceed that level, and by how much?
The 0 mg/L standard still reads 0.020 absorbance. Explain what that nonzero intercept represents and why the calibration line does not pass exactly through the origin.
A very high sample is diluted by mixing equal parts sample and distilled water (a 1-to-1 dilution). The diluted mix reads an absorbance of 0.400. Find the diluted concentration, then the original sample's concentration.
A different sample reads an absorbance of 1.30, above the highest standard (0.970). Explain why you should not trust a concentration read straight off the line, and what you should do instead.
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Answer Key
Answer: 0.095 per mg/L. Slope = (0.970 - 0.020) / (10 - 0) = 0.950 / 10 = 0.095 absorbance per mg/L.
Answer: A = 0.095c + 0.02. The slope is 0.095 and the intercept is the blank reading 0.020.
Answer: 5.0 mg/L. Solve c = (A - 0.02) / 0.095 = (0.495 - 0.02) / 0.095 = 0.475 / 0.095 = 5.0 mg/L.
Answer: 7.0 mg/L. c = (0.685 - 0.02) / 0.095 = 0.665 / 0.095 = 7.0 mg/L.
Answer: No, it is 1.0 mg/L below. The sample is 7.0 mg/L and the alert level is 8.0 mg/L, so it sits 8.0 - 7.0 = 1.0 mg/L under the alert level.
Answer: The 0.020 intercept is the reagent blank, the small amount of color the test chemicals and cuvette add even when no nitrate is present. Because that baseline color exists at zero concentration, the line crosses the absorbance axis above zero instead of at the origin.
Answer: 8.0 mg/L original. The diluted mix reads c = (0.400 - 0.02) / 0.095 = 0.38 / 0.095 = 4.0 mg/L. Because the sample was diluted 1-to-1, the original is twice that, 4.0 x 2 = 8.0 mg/L.
Answer: An absorbance of 1.30 is above the highest standard, so it is outside the range the line was built for, where the response may no longer be linear. You should dilute the sample by a known factor, re-measure, and multiply the result back up.
Differentiation
Support
Provide the plotted calibration line already drawn so students can read concentrations graphically before using the equation, and give the rearranged formula c = (A - 0.02) / 0.095 printed on the handout for items 3, 4, and 7.
Extension
Have students compute the absorbance the equation predicts for each standard, find the difference from the measured value (the residual) at each point, and use those residuals to argue whether a straight line is a good fit across the whole range.
ELL supports
Pre-teach "absorbance," "calibration," "standard," "blank," and "dilution" with a picture sequence showing colorless to deeply colored vials beside the meter. Provide sentence frames for items 6 and 8, such as "The line does not pass through zero because ___."